Question

17. Alexandrina is considering investing in an annuity being offered by Tamu Investments Ltd. The annuity will pay her $7,500 per half year for 6 years. Alexandrina is trying to work out how much this annuity is worth. She thinks she should receive a return equivalent to a nominal interest rate of 6.4% per annum, compounding quarterly. What is the value of this annuity to Alexandrina?

Select one:

a. $74,748.45

b. $73,659.56

c. $71,328.97

d. $72,124.55

Answer 1

17) Interest rate per annum = 6.4% p.a Compounding Quarterly

interest rate Per Quarter = 6.4% /4 = 1.6% per Quarter

Effective interest rate for 6 months =[ ( 1+i/4)^4n-1]*100

Here I = 6.4%

n = 1/2 year ( or ) 0.5 year

Effective interest rate for 6 months =[ ( 1+6.4/400)^4*1/2 - 1] *100

= [( 1+0.016)^2 - 1] *100

= [( 1.016)^2-1] *100

= [ 1.032256-1]*100

= 3.2256%

S.No	Amount	Disc @ 3.2256	Discounted Cash flows
1	$7,500	0.9688	$7,265.64
2	$7,500	0.9385	$7,038.60
3	$7,500	0.9092	$6,818.66
4	$7,500	0.8807	$6,605.59
5	$7,500	0.8532	$6,399.18
6	$7,500	0.8266	$6,199.22
7	$7,500	0.8007	$6,005.50
8	$7,500	0.7757	$5,817.84
9	$7,500	0.7515	$5,636.05
10	$7,500	0.7280	$5,459.93
11	$7,500	0.7052	$5,289.32
12	$7,500	0.6832	$5,124.04
		Total	$73,659.56

Hence Present value of the Annuity is $ 73659.56. So Option b is Correct answer.

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